At the redshift of interest of this work, the escape fraction of Lyman
continuum photons is found to vary over a range of \(0 \lesssim f_{esc}\lesssim 0.29\)  with an average value of \(f_{esc} \sim 0.09\) , as
inferred by the Keck Lyman Continuum Spectroscopic Survey of
star-forming galaxies at \(z \sim 3\) 
[1]}. We further assume \(N_\gamma =9870\) , corresponding to the average metallicity, i.e. log\(Z/Z_{\odot }= -1.5\) , of high redshift DLA absorbers and a Salpeter initial mass
function with \(\alpha = 2.35\) , as given in [2]}. The observed Ly\(\alpha \)  luminosity
also depends on the escape fraction (\(f_{esc}^{Ly{\alpha }}\) ) of Ly\(\alpha \)  photons, and it is related to the emitted Ly\(\alpha \)  luminosity (\(\rm L_{Ly{\alpha }}\) ) as \( L_{Ly{\alpha }}^{obs} = f_{esc}^{Ly{\alpha }}L_{Ly{\alpha }}\) . The Ly\(\alpha \)  escape fraction increases smoothly and
monotonically out to \(z \sim 6\)  and strongly depends on the dust
content [3]}. At the redshift of our
interest the \(f_{esc}^{Ly{\alpha }}\approx 5 \pm 3\%\) , as is estimated
for the high-redshift (\(z \sim 3\) ) star forming galaxies by
[4]}, [3]}.
